Detachments of Amalgamated 3-Uniform Hypergraphs Factorization Consequences
نویسندگان
چکیده
منابع مشابه
On One-factorization of Complete 3-Uniform Hypergraphs
A hypergraph H on n nodes is complete 3-uniform if the hyperedges are precisely the set of all node triples. A one-factor of H is a set of hyperedges that cover each node exactly once. According to Baranyai's proof, the hyperedges of H can be partitioned into one-factors iff n ≡ 0 (mod 3). Though the proof is constructive, it leads to an O(2)-time algorithm. We investigate a method for computin...
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Bollobás and Thomason conjectured that the vertices of any r-uniform hypergraph with m edges can be partitioned into r sets so that each set meets at least rm/(2r − 1) edges. For r = 3, Bollobás, Reed and Thomason proved the lower bound (1− 1/e)m/3 ≈ 0.21m, which was improved to 5m/9 by Bollobás and Scott (while the conjectured bound is 3m/5). In this paper, we show that this Bollobás-Thomason ...
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In this paper we consider the problem of determining all values of v for which there exists a decomposition of the complete 3-uniform hypergraph on v vertices into edge-disjoint copies of a given 3-uniform hypergraph. We solve the problem for each 3-uniform hypergraph having at most three edges and at most six vertices, and for the 3-uniform hypergraph of order 6 whose edges form the lines of t...
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A conjecture of Bollobás and Thomason asserts that, for r ≥ 1, every r-uniform hypergraph with m edges can be partitioned into r classes such that every class meets at least rm/(2r−1) edges. Bollobás, Reed and Thomason [3] proved that there is a partition in which every edge meets at least (1 − 1/e)m/3 ≈ 0.21m edges. Our main aim is to improve this result for r = 3. We prove that every 3-unifor...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Designs
سال: 2012
ISSN: 1063-8539
DOI: 10.1002/jcd.21310